Question

The sum of the cubes of consecutive natural numbers gives the _______ of _________ numbers.

• A. cubes, triangular
• B. squares, prime
• C. squares, triangular
• D. cubes, prime

Answer 1

The correct option is C squares, triangular

The triangular number sequence is 1, 3, 6,10, 15, 21 and so on..
Let us take the sum of the cubes of the 1st two natural numbers:
$1^3$ + $2^3$ = 1 + 8 = 9 = $3^2$ ( 3 is a triangular number)
Similarly, $1^3$ + $2^3$ + $3^3$ = 1 + 8+ 27 = 36 = $6^2$ ( 6 is a triangular number)
Generalising the above we can say that the sum of the cubes of consecutive natural numbers gives the squares of triangular numbers.